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<title>Gaborator Example 4: Measuring the Signal-to-Noise Ratio</title>
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<h1>Example 4: Measuring the Signal-to-Noise Ratio</h1>

<h2>Introduction</h2>

<p>This example measures the signal-to-noise ratio (SNR) of the
resynthesis by analyzing and resynthesizing a test signal
and comparing the resynthesis result to the original.
</p>

<p>Since it does not involve any audio file I/O, this example
does not require the sndfile library, making it the shortest
and simplest one by far.</p>

<h2>Preamble</h2>

<pre>
#include &lt;iostream&gt;
#include &lt;iomanip&gt;
#include &lt;random&gt;
#include &lt;gaborator/gaborator.h&gt;
</pre>

<h2>Amplitude Measurement</h2>
<p>To calculate the signal-to-noise ratio, we need to measure the
amplitude of the orignal signal and the error residue.  We will use
the root-mean-square amplitude, which is calculcated by the
function <code>rms()</code>.
</p>
<pre>
double rms(const std::vector&lt;float&gt; &amp;v) {
    double sqsum = 0;
    for (size_t i = 0; i &lt; v.size(); i++) {
        sqsum += v[i] * v[i];
    }
    return sqrt(sqsum);
}
</pre>

<h2>Main Program</h2>

<p>For the test signal, we use a million samples of white noise with a
uniform amplitude distribution between -1 and +1.</p>
<pre>
int main(int argc, char **argv) {
    size_t len = 1000000;
    std::vector&lt;float&gt; signal_in(len);
    std::minstd_rand rand;
    std::uniform_real_distribution&lt;&gt; uniform(-1.0, 1.0);
    for (size_t i = 0; i &lt; len; i++)
        signal_in[i] = uniform(rand);
</pre>
<p>Then we create a spectrum analyzer with 48 bands per octave
and a frequency range of 3 decades (0.0005 to 0.5 times the sample rate):</p>
<pre>
    gaborator::parameters params(48, 5e-4);
    gaborator::analyzer&lt;float&gt; analyzer(params);
</pre>
<p>...and run the spectrum analyzis:</p>
<pre>
    gaborator::coefs&lt;float&gt; coefs(analyzer);
    analyzer.analyze(signal_in.data(), 0, len, coefs);
</pre>
<p>...resynthesize the signal into <code>signal_out</code>:
<pre>
    std::vector&lt;float&gt; signal_out(len);
    analyzer.synthesize(coefs, 0, len, signal_out.data());
</pre>
<p>...measure the resynthesis error:</p>
<pre>
    std::vector&lt;float&gt; error(len);
    for (size_t i = 0; i &lt; len; i++)
         error[i] = signal_out[i] - signal_in[i];
</pre>
<p>...calculate the signal-to-noise ratio:</p>
<pre>
    double snr = rms(signal_in) / rms(error);
</pre>
<p>...and print it in decibels:</p>
<pre>
    std::cout << std::fixed << std::setprecision(1) << 20 * log10(snr) << " dB\n";
}
</pre>
<h2>Compiling</h2>
<p>Like <a href="render.html#compiling">Example 1</a>, this example
can be built using a one-line build command:
</p>
<pre class="build Darwin Linux NetBSD FreeBSD">
c++ -std=c++11 -I.. -O3 -ffast-math `pkg-config --cflags sndfile` snr.cc `pkg-config --libs sndfile` -o snr
</pre>
<p>Or using the vDSP FFT on macOS:</p>
<pre class="build Darwin">
c++ -std=c++11 -I.. -O3 -ffast-math -DGABORATOR_USE_VDSP `pkg-config --cflags sndfile` snr.cc `pkg-config --libs sndfile` -framework Accelerate -o snr
</pre>
<p>Or using PFFFT (see <a href="render.html#compiling">Example 1</a> for how to download and build PFFFT):</p>
<pre class="build">
c++ -std=c++11 -I.. -Ipffft -O3 -ffast-math -DGABORATOR_USE_PFFFT `pkg-config --cflags sndfile` snr.cc pffft/pffft.o pffft/fftpack.o `pkg-config --libs sndfile` -o snr
</pre>

<h2>Running</h2>
<p>The program is run with no arguments:</p>
<pre class="run">
./snr
</pre>
<p>This will print the SNR which should be more than 100 dB if the library is working correctly.</p>

<div class="nav"><span class="prev"><a href="stream.html">Previous: Example 3: Streaming</a></span><span class="next"><a href="synth.html">Next: Example 5: Synthesis from Scratch</a></span></div>

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